We consider the pseudo-Euclidean space (Rn,g)\documentclass[12pt]{minimal}
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\begin{document}$$({\mathbb {R}}^n,g)$$\end{document}, with n≥3\documentclass[12pt]{minimal}
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\begin{document}$$n \ge 3$$\end{document} and gij=δijεi\documentclass[12pt]{minimal}
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\begin{document}$$g_{ij} = \delta _{ij} \varepsilon _{i}$$\end{document}, where εi=±1\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon _{i} = \pm 1$$\end{document}, with at least one positive εi\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon _{i}$$\end{document} and non-diagonal symmetric tensors T=∑i,jfij(x)dxi⊗dxj\documentclass[12pt]{minimal}
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\begin{document}$$T = \sum \nolimits _{i,j}f_{ij}(x) dx_i \otimes dx_{j} $$\end{document}. Assuming that the solutions are invariant by the action of a translation (n-1)\documentclass[12pt]{minimal}
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\begin{document}$$(n-1)$$\end{document}- dimensional group, we find the necessary and sufficient conditions for the existence of a metric g¯\documentclass[12pt]{minimal}
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\begin{document}$$\bar{g}$$\end{document} conformal to g, such that the Schouten tensor g¯\documentclass[12pt]{minimal}
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\begin{document}$$\bar{g}$$\end{document}, is equal to T. From the obtained results, we show that for certain functions h, defined in Rn\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {R}^{n}$$\end{document}, there exist complete metrics g¯\documentclass[12pt]{minimal}
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\begin{document}$$\bar{g}$$\end{document}, conformal to the Euclidean metric g, whose curvature σ2(g¯)=h\documentclass[12pt]{minimal}
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\begin{document}$$\sigma _{2}(\bar{g}) = h$$\end{document}.
